Mechanics - Newtonian Mechanics

• Deals with the effects of forces on objects and the resulting motion

• Two smaller categories

  • Kinematics

    • “Description of Motion”

  • Dynamics

    • “Cause of Motion”

Kinematics

• There are three ways we talk about motion

  • Words

    • Time

    • Distance, Displacement

    • Speed, Velocity

    • Acceleration

  • Graphs / Diagrams

  • Equations

Guidelines for Studying Motion

• We will look at objects as if they are single point objects. We will use the center of mass. (CM)

• We will start with motion in just one dimension

• Study each motion independently

  • At rest

  • Constant

  • Accelerated

• Motions diagrams are nothing more than points that are spaced at intervals to represent the motion of an object. Every point represents the position of the object, but also represents an equal time interval

Where To Start

• Motion is defined as the change in position of some object relative to some stationary point

• Position

  • Where object is relative to your coordinate origin (Vector)

    • Cartesian (rectangular / component form) — (x, y)

    • Polar (magnitude and angle form) — (r, theta)

• Stationary Points

  • Reference Points

    • A collection of all the reference points used to study an object is called frame of reference

  • Points you pick as an observer and say are stationary

• Motion is relative

Distance vs. Displacement

• Distance (d)

  • The total path the object travels

  • Length units:

    • m, ft, mi, km, in

• Displacement (Δd)

  • Change in position

  • How far away you end up from where you start

    • Straight line

  • Vector - Needs #, unit, and direction

    • Length units

      • m, ft, mi, km, in

    • Direction

      • N, S, E, W, Up, Down, Right, Left, or +/-

• Displacement can never be bigger than the distance, but distance can be greater than the displacement

Speed vs. Velocity

• Speed

  • How fast or slow an object is moving

  • Average speed is the ratio of total distance traveled to the time interval

  • Units:

    • mi/hr, km/hr, ft/s, m/s

  • 3 types of speed

    • Constant speed

    • Average speed

    • Instantaneous speed

• Velocity

  • Rate of change in displacement

  • Speed with direction

  • Units:

    • mi/hr, km/hr, ft/s, m/s

  • Velocity Direction == Displacement Direction

  • 3 types of velocity

    • Constant velocity

    • Average velocity

    • Instantaneous velocity

Variable vs. Time Graphs

Speed vs. Time Graphs

• The slope of a position (displacement) vs. time graph is the speed

  • The slope of a tangent to a position vs. time graph is instantaneous speed

Position vs. Time Graphs

• Curve

• Diagonal

• Horizontal

• Zero

Acceleration

• How fast something increases or decreases velocity

• The rate of change in velocity

• Is a vector - #, unit, direction

  • Units: mi/hr², km/hr², ft/s², m/s²

• Can be positive or negative

• When velocity and acceleration = same direction = object speeding up

• Velocity direction ≠ Acceleration direction = object slowing down

3 Types of Acceleration

• Constant (uniform) acceleration

  • A uniform increase or decrease in velocity

• Average acceleration

  • The rate of change in velocity

• Instantaneous acceleration

  • The acceleration of an object at a given instant in time